Mathematical Sciences: Geometric Approach to Weinstein Conjecture

首席研究员将研究是否存在 紧密接触叶理 流形 这些叶理的存在是由 温斯坦 几个特殊的案件已经解决了这一点 研究人员和其他数学家。 利科里什外科 技术将被用来研究三维 问题的版本。 Okumura的理论将被应用于 问题的情况下，超曲面的接触类型， 凯勒流形 还将研究单同态群。 “流形”是广义曲面。 这些可能会被填充 低维“叶子”的集合。“这些收藏品 称为“叶状体”。“首席研究员 我会研究那些不连续缠绕的叶子， 靠近点。 在文献中被称为“紧密叶。" 这在其他科学的应用中尤为重要 在一般意义上，它们代表了 无限期重复。

The principal investigator will study the existence of compact leaves in contact foliations of compact contact manifolds. The existence of these foliations was conjectured by Weinstein. Several special cases have been solved by this investigator and by other mathematicians. Lickorish surgical techniques will be used to investigate the three-dimensional version of the problem. Okumura's theory will be applied to the problem in the case of hypersurfaces with contact types in Kaehler manifolds. Diffeomorphism groups will also be studied. "Manifolds" are generalized surfaces. These may be filled with collections of lower dimensional "leaves." Such collections of leaves are called "foliations." The principal investigator will study leaves which do not wrap on continuously but actually close up. These are called in the literature, "compact leaves." Such are particularly important in applications to other sciences in that they represent, in a general sense, behavior which repeats indefinitely.